[2] The type and only known species is R. stovalli, found from the Early Permian Fairmont Shale in Cleveland County, Oklahoma.

Citing what is currently Article 39 of the International Code of Zoological Nomenclature, Zanon (1988)[2] pointed out that if any family is to bear the name Goniorhynchidae, it must be based on the valid genus Goniorhynchus Hampson, 1896, not on the invalid Goniorhynchus Olson, 1970; he therefore coined the replacement name Rhynchonkidae, which has been used in some works.

[11][12] Rhynchonkos shares many features with the early caecilian Eocaecilia, including an elongated snout, small limbs, and a similar skull.

[5] Carroll and Currie (1975), the first to suggest this possible relationship, noted similarities in temporal fenestration, palatal structure, braincase composition, and mandibular dentition.

Carroll and Currie also mentioned that Rhynchonkos and caecilians have a pleurosphenoid that joins the otic-occipital portion of the braincase with the sphenethmoid, a characteristic which they considered unique among amphibians.

The adjacent tooth rows on the coronoid and the dentary of Rhynchonkos were also considered a characteristic that linked it with caecilians.

[14] Despite these similarities, many of the characteristics that suggested a close relationship between Rhynchonkos and caecilians have since been considered primitive, convergent, or indeterminate.